Goldeneye is probably too obvious choice when it comes down to it. Was great for its day and still a classic.
If I had to choose a different game though, I would say Quake III Arena or the first Unreal Tournament.
Not only were they one of the high points in PC FPS multiplayer gaming like a decade ago, but the Dreamcast and PS2 ports were exceptionally well done too. My personal pick, the Dreamcast being the better of the two even if both games had some cut down features compared to the PC/PS2 versions, i.e. less bots or none of the huge levels due to system memory limitations.
The sharper graphics, much better controls (Xbox-to-Xbox360 pad is just a refinement of the Dreamcast pad!) and mouse and keyboard controls too which was quite a first for a console. And not to mention, the first FPS on console online play!
Such a shame for the little white box though, it was too ahead of its time back then.